Distributions pp 321-347 | Cite as

Appendix: Integration

Part of the Cornerstones book series (COR)


As we have seen, in Theorems 3.15 and 3.18 above, continuous linear forms on C 0.(X), for X an open subset of C n, arise naturally in the theory of distributions. The alternative name of Radon measure for such a form finds its origin in the existence of a bijective correspondence that associates a complex-valued measure on X to the linear form. More specifically, we have the following (Frigyes)1 Riesz Representation Theorem.


Linear Form Integrable Function Cauchy Sequence Bounded Variation Nonnegative Function 
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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Mathematical InstituteUtrecht UniversityUtrechtThe Netherlands

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